CN108737301A - A kind of broadband connections transmitter fingerprint method of estimation based on B-spline neural network - Google Patents
A kind of broadband connections transmitter fingerprint method of estimation based on B-spline neural network Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/0212—Channel estimation of impulse response
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
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- H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
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- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
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- H04L25/0254—Channel estimation channel estimation algorithms using neural network algorithms
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Abstract
The broadband connections transmitter fingerprint method of estimation based on B-spline neural network that the present invention relates to a kind of.This method estimates transmitter IQ imbalances parameter combination and nonlinear B-spline neural network model coefficient according to ofdm signal is received, and constitutes two-dimensional feature vector as communication transmitter fingerprint, is used for the authentication of communication equipment.Show that this method is preferable to the discrimination of high hardware similarity transmitter, can be applied to the occasions such as the certification of physical layer high intensity and the anti-counterfeiting of ofdm communication equipment from theory deduction and numerical simulation classification experiments.
Description
Technical field
The present invention relates to a kind of broadband connections transmitter fingerprints being based on B-spline neural network (B-Spline neural networks)
Method of estimation.
Background technology
In recent years, with the rapid development of the technologies such as artificial intelligence, Internet of Things, 5G, the safety of physical layer of communication network is
As the research hotspot of wireless communication related field.Recognizing for communication user is carried out using the hardware characteristics of communication transmitter as fingerprint
Card is a research direction of safety of physical layer.
It is found through retrieval, document (Yuan Honglin, Hu Aiqun, old unique Journal of Sex Research [J] applied science for opening will radio-frequency fingerprints
Journal, 2009,27 (1):Communication transmitter radio-frequency fingerprint 1-5.) is had studied only by mathematical modeling under the conditions of high sampling rate
One property has obtained the conclusions such as the principal element for influencing radio-frequency fingerprint uniqueness.
Document (Liang Yan, Shu Feng, Zhang Yijin, wait in Sparse multi-path channel environment the IQ imbalances of MIMO-OFDM systems and
Channel Combined estimator [J] electronics and information journal, 2013,35 (2):It 280-284.) has studied a kind of while estimating ofdm system
The method of transmitter and receiver IQ imbalances and channel.
Above-mentioned document describes the uniqueness of communication transmitter radio-frequency fingerprint, and discloses some identification transmitter radio frequencies and refer to
The method of line.That there are accuracy of identification is not high for these methods, generally requires high sampling rate, high bandwidth and high quantization precision, is not suitable for
In extensive use.
Invention content
To solve above-mentioned deficiency in the prior art, it is logical that the present invention proposes a kind of broadband based on B-spline neural network
Believe transmitter fingerprint method of estimation.Specifically technical solution is：Reception estimation and the feature of fingerprint are completed on communication control processor
Extraction, steps are as follows：
1st step：Docking receipts signal frame carries out cyclic prefix and operates, and result is time domain discrete signal phasor r, further according to
The symmetrical subset s of conjugation of ofdm communication frame frequency domain symbolic vectorAWith conjugate antisymmetry subset sBIt decomposes vector r and obtains rAWith rB；
2nd step：The linear approximation amplification factor set of transmitter nonlinear PA is setM
For maximum iteration, linear approximation amplification factor serial number m initial values are 1；
3rd step：Linear approximation amplification factor is arranged to estimate
4th step：According to the symmetrical subset s of conjugationAMulti-path channel impulse response estimation is carried out, formula is：
And it is rightThe estimation of h is obtained into row interpolation
Wherein diagIndicate sAThe diagonal matrix that each element is constituted, { }-indicate inverse matrix, hAIndicate sACorresponding multipath channel
Impulse response, DFT { rAIndicate rADiscrete Fourier transform；
5th step：According to conjugate antisymmetry subset sBThe estimation of IQ imbalance parameter combinations is carried out, formula is：
Wherein, ε withThe respectively amplitude imbalance degree and phase deviation of I/Q modulator, E { } expressions are averaged operation, and/
Indicate that the point of vector element removes, ΛBIndicate that handle passes through sAThe channel impulse response estimated carries out interpolation and is then spaced a channel
Diameter number extracts the channel impulse response after half, DFT { rBIndicate rBDiscrete Fourier transform；
6th step：The approximate mean power of noise w is calculated, formula is：
Wherein,According toThe time domain channel circular matrix of structure,WHFor
The transposed matrix of Discrete Fourier transform, (WHs)*Indicate WHThe complex conjugate operation result of s；S is OFDM pilot tone frequency domain datas
Vector, N are complex data number, | | indicate modulo operation；
7th step：M is from adding 1, if m is not equal to M+1, returns to the 3rd step and repeats；If m is equal to M+1, repeated work knot
Beam continues to execute downwards；
8th step：Search E | w |2}mMinimum value min (E | w |2}m)=E | w |2}q, then at this point, IQ imbalance parameter groups
The estimated value of conjunction
9th step：Calculate the estimation of time domain discrete ofdm signal vector：
Wherein,
10th step：The nonlinear characteristic ψ () of transmitter is modeled using complex value B-spline neural network, the nerve net
Network answers the estimated value of weight coefficient vector θ：
Wherein, ()+Indicate pseudo-inverse operation,According toThe B-spline basic matrix estimation of structure,For time domain channel arteries and veins
The circular matrix estimation of punching response h；
11st step：It is rightMould carry out the similar factors feature f based on rectangle respectivelyrecWith the similar factors feature of triangle
ftriExtraction, formula are：
Wherein,ForMould, rec and tri indicate rectangle and DELTA vectors respectively,<,>Indicate inner product operation, | | | |
Indicate the Euclidean length of vector；
12nd step：Calculate the estimation of IQ imbalancesWith the similar factors feature f of rectanglerecThe F of compositionrecVector, and
IQ imbalances are estimatedWith the similar factors feature f of triangletriThe F of compositiontriVector, i.e.,：
It is described to calculate FrecAnd FtriThe two-dimensional vector of composition is the fingerprint vector of transmitter for identification.
The present invention compared with the prior art, according to receive orthogonal frequency division multiplexing (Orthogonal Frequency
Division Multiplexing, OFDM) signal estimates transmitter IQ imbalances parameter combination and nonlinear B-spline god
Through network model coefficient, and constitutive characteristic vector is used for the authentication of communication equipment as communication transmitter fingerprint.The present invention
The sampling rate that the method for proposition needs is identical as OFDM frequency domain symbol rates, and resolution is apparently higher than conventional method.
Description of the drawings
Fig. 1 is that communication transmitter fingerprint proposed by the present invention receives system model figure.
Fig. 2 is the Nonlinear Characteristic Curve figure of PA in experiment.
Fig. 3 is in experiment, by the design sketch of normalization planisphere identification.
Fig. 4 is in experiment, by the characteristic vector distributed effect figure of the method for the present invention identification.
Fig. 5 is to identify transmitter correct recognition rata line chart in experiment to press the method for the present invention.
Specific implementation mode
To make the objectives, technical solutions, and advantages of the present invention more comprehensible, right below in conjunction with attached drawing and implementation process
The present invention is further elaborated.
Fig. 1 is that a communication transmitter fingerprint receives system model, including ofdm communication transmitter section, impulse response are
The multipath channel and fingerprint receiving portion of h (t).
1, ofdm communication transmitter section
Including ofdm signal generator, digital analog converter (Digital to Analog Converter, DAC), IQ modulation
Device, nonlinear power amplifier (Power Amplifier, PA), the course of work is as follows：
After OFDM pilot tone data d enters the ofdm signal generator, two-way quadrature discrete signal is exported；It passes through again
After crossing digital analog converter described in two-way, the real part i (t) and imaginary part q (t) of continuous signal x (t), the continuous signal x are generated respectively
(t) expression formula is：X (t)=i (t)+jq (t)；
Then, the real part of x (t) becomes modulated signal x after I/Q modulator respectively with imaginary partIQ(t), the signal xIQ(t)
Expression formula be：
xIQ(t)=G1x(t)+G2x*(t),
Wherein, * indicate complex conjugate operation, ε withThe respectively amplitude imbalance degree and phase deviation of I/Q modulator, it is ideal
In the case of ε=1 with
Then, the signal xIQ(t) become amplified signal x after PAPA(t), the signal xPA(t) expression formula is：
Wherein, ψ () indicates that nonlinear characteristic, A () and φ () indicate that the amplitude response of non-linear PA is rung with phase respectively
It answers, | | expression takes amplitude, ∠ expressions to take phase angle.If a indicates amplitude, the definition of A (a) and φ (a) and is
Wherein, gαFor small gain signal, βαFor smoothing factor, AsatFor saturation level, αφ、βφ、q1With q2For adjustable parameter.
The operating point of PA is by peak power output PmaxWith average output power PmeanThe ratio between, i.e. output rollback (Output
Back-Off, OBO) it determines, it is defined as
OBO is smaller, then the operating point of PA is closer to saturation region.
2, multipath channel part
Communication channel multipath channel is to simulate actual transmission channel, if the impulse response vector of multipath channel is：
H=[h0,h1,…hL]T
Wherein, L+1 is the multipath channel diameter number less than ofdm signal circulating prefix-length, and sets h0=1.
The time domain discrete ofdm signal received after the transmission is r (n), and the expression formula of the signal r (n) is：
Wherein,Indicate that the overturning of channel impulse response, periodic extension are operated with main value is taken, w (n) for from
Dissipate additive white Gaussian noise signal；
3, fingerprint receiving portion
Initialization：Docking receipts signal frame carries out cyclic prefix and operates, and result is time domain discrete signal phasor r, further according to
The symmetrical subset s of conjugation of ofdm communication frame frequency domain symbolic vectorAWith conjugate antisymmetry subset sBIt decomposes vector r and obtains rAWith rB；If
Set the nonlinear linear approximation amplification factor set of transmitter PAM is maximum iteration,
Linear approximation amplification factor serial number m initial values are 1.
It repeats：
Linear approximation amplification factor is arranged to estimate
According to the symmetrical subset s of conjugationAMulti-path channel impulse response estimation is carried out, formula is：
Wherein { }-Indicate inverse matrix, and rightThe estimation of h is obtained into row interpolationDiag indicates sAEach element is constituted diagonal
Matrix, hAIndicate sACorresponding multi-path channel impulse response, DFT { rAIndicate rADiscrete Fourier transform；
According to conjugate antisymmetry subset sBThe estimation of IQ imbalance parameter combinations is carried out, formula is：
Wherein, ε withThe respectively amplitude imbalance degree and phase deviation of I/Q modulator, E { } indicate operation of averaging ,/expression vector
The point of element removes, ΛBIndicate that handle passes through sAThe channel impulse response estimated carries out interpolation and is then spaced a channel diameter number extraction
Channel impulse response after half；DFT{rBIndicate rBDiscrete Fourier transform；
The approximate mean power of noise w is calculated, formula is：
Wherein,According toThe time domain channel circular matrix of structure,WHIt is discrete
The transposed matrix of Fourier transform matrix, (WHs)*Indicate WHThe complex conjugate operation result of s；S swears for OFDM pilot tone frequency domain datas
Amount, N are complex data number, | | indicate modulo operation；
M=m+1；
Until：M=M+1.
Output：Search E | w |2}mMinimum value min (E | w |2}m)=E | w |2}q, then at this point, IQ imbalance parameter groups
The estimated value of conjunction
Calculate the estimation of time domain discrete ofdm signal vector：Wherein,
The nonlinear characteristic ψ () of transmitter is modeled using complex value B-spline neural network, which weighs again is
The estimated value of number vector theta：Wherein, ()+expression pseudo-inverse operation,According toThe B-spline group moment of structure
Battle array estimation,The circular matrix estimation of h is responded for time domain channel impulse；
It is rightMould carry out the similar factors feature f based on rectangle respectivelyrecWith the similar factors feature f of triangletriIt carries
It takes, formula is：Wherein,ForMould, rec and tri indicate respectively rectangle with
DELTA vectors,<,>Indicate inner product operation, | | | | indicate the Euclidean length of vector；
Calculate the estimation of IQ imbalancesWith the similar factors feature f of rectanglerecThe F of compositionrecVector and IQ are uneven
EstimationWith the similar factors feature f of triangletriThe F of compositiontriVector, i.e.,：
It is described to calculate FrecAnd FtriThe two-dimensional vector of composition is the fingerprint vector of transmitter for identification.
Present invention applicant carries out following experiments to verify the recognition effect of this bright method.
When experiment, randomly generate by being conjugated the symmetrical ofdm signal that yoke antisymmetry pilot tone symbol is constituted together, modulation
Scheme uses 16-QAM, FFT a length of 2048, cyclic prefix length 512.And the multipath channel for setting 3 communication transmitters it is identical and
It is constant when within the algorithm time.
1, transmitter hardware parameter is arranged
If 3 transmitters use " transmitter -1 ", " transmitter -2 " and " transmitter -3 " to indicate respectively.The amplitude of transmitter with
Phase IQ imbalance parameters be respectively ε withThe parameter of the memoryless non-linear PA of transmitter is
βα=0.81 (1+ △), Asat=1.4 (1+ △), βφ=0.123 (1+ △),
q1=3.8 (1+ △), q2=3.7 (1+ △)
Wherein, △ is nonlinear parameter.Each parameter setting values of 3 transmitters are as shown in table 1 in experiment.
1 transmitter IQ imbalances of table and PA parameters
When transmitter is without IQ imbalances ε=1.00 andAs shown in Table 1, the hardware differences of 3 transmitters are very
It is small.Nonlinear Characteristic Curve figure according to 3 transmitter PA of the setting of table 1 is as shown in Figure 2.The OBO of 3 transmitters is on the left sides 7.5dB
It is right.Design sketch such as Fig. 3 institutes that communication training frames symbol after 3 transmitters of arrangement above is identified by normalization planisphere
Show.From the figure 3, it may be seen that the artificial difference that can not tell 3 transmitter symbol planispheres substantially.
From the foregoing, it will be observed that 3 transmitter not only meets digital communication requirement, but also meets in communication transmitter finger print identifying and lead to
Letter equipment be usually same model with a series of stringent condition.
2, transmitter fingerprint classification
Document (Hong X, Chen S, Gong Y, et al.Nonlinear Equalization of are used in experiment
Hammerstein OFDM Systems[J].IEEE Transactions on Signal Processing,2014,62
(21):Rayleigh multidiameter fading channels in 5629-5639.), multipath diameter number are L+1=10, and the mean power of l diameters is
0≤l≤L, wherein λ is the fading channel factor.
The signal of constellation shown in Fig. 3 after multipath channel h with additive white Gaussian noise (Additive White
Gaussian Noise, AWGN) superposition, then reach transmitter fingerprint receiver.
The B-spline neural network constituted using four B-spline basic functions, the quantity of B-spline basic function are set as 8, node
Sequence be -16.6667, -15.0000, -0.5000, -0.1667, -0.0833, -0.0333,0,0.0333,0.0833,
0.1667,0.5000,15.0000,16.6667 }.
As signal-to-noise ratio EbN0When=10dB, the 66 independent AWGN noises and corresponding receive that generate 3 transmitters respectively are believed
Number, 66 reception sample of signal of 3 receivers of simulation.According to this 3 groups of reception sample of signal, emitted using communication proposed in this paper
Machine fingerprint method of estimation obtains the IQ imbalance fingerprints of 3 transmitters respectivelyWith non-linear fingerprintIt is rightCarry out rectangle with
The similar factors feature extraction of triangle, respectively withThe characteristic vector F of constructionrecWith FtriDistribution is as shown in Figure 4.
As shown in Figure 4, the characteristic vector F of 3 transmitterrecWith FtriIt is nearest using basic k with certain separability
Adjacent (k-Nearest Neighbor, k-NN) classification carries out classification experiments.Preceding 33 sample composing trainings of each transmitter
Collection, rear 33 samples are as test set.The k of k-NN graders takes 1 to 4, is based on FrecWith FtriObtained correct classification rate such as table 2
It is shown.
2 correct Classification and Identification rate of table
Unit/%
As shown in Table 2, it is based on transmitter IQ imbalances and the non-linear vector similar factors features of PA, using k-NN graders
Obtained 3 transmitter realizes sample in EbN0For 10dB when correct classification rate be about 70%.
E is setbN0From 0dB to 30dB, it is divided into 5dB, each EbN0100 Monte Carlo classification experiments of lower progress,
The correct classification rate that independent experiment obtains is averaged, the results are shown in Figure 5.As shown in Figure 5, feature based vector FrecWith
Ftri, correct recognition rata is with EbN0Increase and increase, work as EbN0For 10dB when, identification correct recognition rata be about 70%；Work as EbN0For
When 15dB, correct recognition rata basically reaches 90%.And the discrimination of two kinds of characteristic vectors is without evident regularity, the k of k-NN graders
Value is with discrimination also without evident regularity.
It is derived with the simulation experiment result by above-mentioned theory it is found that this method is to high hardware similarity ofdm communication transmitter
Discrimination is preferable, can be applied to the occasions such as the certification of physical layer high intensity and the anti-counterfeiting of ofdm communication equipment.In addition this method makes
Sampling rate is identical as baseband frequency-domain character rate, and than traditional high sampling rate recognition methods, practicability is also stronger.
Claims (1)
1. a kind of broadband connections transmitter fingerprint method of estimation based on B-spline neural network, which is characterized in that in communications reception
The reception estimation and feature extraction that fingerprint is completed on machine, are as follows：
1st step：Docking receipts signal frame carries out cyclic prefix and operates, and result is time domain discrete signal phasor r, logical further according to OFDM
Believe the symmetrical subset s of conjugation of frame frequency domain symbolic vectorAWith conjugate antisymmetry subset sBIt decomposes vector r and obtains rAWith rB；
2nd step：The linear approximation amplification factor set of transmitter nonlinear PA is setM is most
Big iterations, linear approximation amplification factor serial number m initial values are 1；
3rd step：Linear approximation amplification factor is arranged to estimate
4th step：According to the symmetrical subset s of conjugationAMulti-path channel impulse response estimation is carried out, formula is：
And it is rightThe estimation of h is obtained into row interpolation
Wherein diag indicates sAThe diagonal matrix that each element is constituted, { }-Indicate inverse matrix, hAIndicate sACorresponding multi-path channel impulse is rung
It answers, DFT { rAIndicate rADiscrete Fourier transform；
5th step：According to conjugate antisymmetry subset sBThe estimation of IQ imbalance parameter combinations is carried out, formula is：
Wherein, ε withThe respectively amplitude imbalance degree and phase deviation of I/Q modulator, E { } indicate operation of averaging ,/expression
The point of vector element removes, ΛBIndicate that handle passes through sAThe channel impulse response estimated carries out interpolation and is then spaced a channel diameter number
Extract the channel impulse response after half, DFT { rBIndicate rBDiscrete Fourier transform；
6th step：The approximate mean power of noise w is calculated, formula is：
Wherein,According toThe time domain channel circular matrix of structure,WHIt is discrete
The transposed matrix of Fourier transform matrix, (WHs)*Indicate WHThe complex conjugate operation result of s；S swears for OFDM pilot tone frequency domain datas
Amount, N are complex data number, | | indicate modulo operation；
7th step：M is from adding 1, if m is not equal to M+1, returns to the 3rd step and repeats；If m is equal to M+1, repeated work terminates, after
It is continuous to execute downwards；
8th step：Search E | w |2}mMinimum value min (E | w |2}m)=E | w |2}q, then at this point, IQ imbalance parameter combinations
Estimated value
9th step：Calculate the estimation of time domain discrete ofdm signal vector：
Wherein,
10th step：The nonlinear characteristic ψ () of transmitter is modeled using complex value B-spline neural network, the neural network is multiple
The estimated value of weight coefficient vector θ：
Wherein, ()+expression pseudo-inverse operation,According toThe B-spline basic matrix estimation of structure,For time domain channel impulse
Respond the circular matrix estimation of h；
11st step：It is rightMould carry out the similar factors feature f based on rectangle respectivelyrecWith the similar factors feature f of triangletri
Extraction, formula are：
Wherein,ForMould, rec and tri indicate rectangle and DELTA vectors respectively,<,>Indicate inner product operation, | | | | it indicates
The Euclidean length of vector；
12nd step：Calculate the estimation of IQ imbalancesWith the similar factors feature f of rectanglerecThe F of compositionrecVector and IQ are uneven
Weighing apparatus estimationWith the similar factors feature f of triangletriThe F of compositiontriVector, i.e.,：
It is described to calculate FrecAnd FtriThe two-dimensional vector of composition is the fingerprint vector of transmitter for identification.
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| CN113037726A (en) * | 2021-02-26 | 2021-06-25 | 南通大学 | Radio frequency fingerprint authentication method of broadband communication equipment based on Kronecker product parameter separation |
| CN113515259A (en) * | 2021-05-24 | 2021-10-19 | 西安电子科技大学 | Complex number approximate modulus realization circuit and method suitable for floating point format |
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| CN113037726A (en) * | 2021-02-26 | 2021-06-25 | 南通大学 | Radio frequency fingerprint authentication method of broadband communication equipment based on Kronecker product parameter separation |
| CN113037726B (en) * | 2021-02-26 | 2021-10-26 | 南通大学 | Radio frequency fingerprint authentication method of broadband communication equipment based on Kronecker product parameter separation |
| CN113515259A (en) * | 2021-05-24 | 2021-10-19 | 西安电子科技大学 | Complex number approximate modulus realization circuit and method suitable for floating point format |
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